[hamdani yusuf (OP)]

Counterbalanced forces indicates equal and opposite forces while cancellation of force indicates it's removal- not the same thing at all. The girl on the scales maintains her downward force due to gravity, similarly a torque which fails to produce rotation is still a torque.

What do you call it in the case below? Cancel out or counterbalance?

...


Here's another example to show that expected rotational radius is not always the same as the real rotational radius.
It's similar to previous case, but this time a solid object is obstructing the rotation.
The question is, what's the torque produced by the force?

[hamdani yusuf (OP)]

Which table are you referring to?

All of them. Apples are not oranges.

Consider a simple case. Momentum is a vector in the direction of motion. Angular momentum is a vector, but nothing is moving in the direction of the vector.

Most of the values contained in the tables are identical with existing widely accepted standard. If your assertion is correct, then they are far from perfect, as you claimed in the poll. You are contradicting yourself.

[hamdani yusuf (OP)]

BC, he will not answer your question. He tries to divert the discourse when questioned after saying something he cannot back up. He has avoided my question, re the "cancellation" of force.

I know. And that's why I can't understand why the mods don't ban him.

Perhaps because they already understand my point. You are wondering why because you haven't yet.

You.
Did.
Not.
Answer.

Read my answer in reply#863. If you can't understand it, that's your problem.

[hamdani yusuf (OP)]

One thing that has become clear is that chatbots do not understand the concept or use of dimensions, and in the case of Gemini, is even capable of generating lies: 

torque is a force resulting from rotation

indeed!

Nor, it seems, are chatbots or ignorant educationalists aware of the difference between a scalar (energy) and a vector (torque). I'll admit to possibly having added to the confusion by occasionally writing F . r when the conventional representation should be F x r. No excuse, but in mitigation the number we use is of course the magnitude of the product.

So my advice is to ignore anything but your own common sense, experience, understanding of basic physics and mathematics, and the standard nomenclature that everyone else uses.

The statement that you quoted is from a user of stackexchange.com, not Gemini itself. You need to read more carefully next time.

I've also mentioned about the distinction between cross product and dot product earlier in this thread.

If you've already used your own common sense, experience, understanding of basic physics and mathematics, and the standard nomenclature that everyone else uses, but still come into a wrong conclusion, then you need to check your underlying assumptions you've used to make that conclusion.

[paul cotter]

The only one coming to wrong conclusions is YOU.

[Bored chemist]

BC, he will not answer your question. He tries to divert the discourse when questioned after saying something he cannot back up. He has avoided my question, re the "cancellation" of force.

I know. And that's why I can't understand why the mods don't ban him.

Perhaps because they already understand my point. You are wondering why because you haven't yet.

You.
Did.
Not.
Answer.

Read my answer in reply#863. If you can't understand it, that's your problem.

That's the post in which you quoted me saying "(or, if you want, slightly higher)." but ignored it.
So.
Stop wasting time with nonsense about Cavendish's torsion balance- which is very clever but irrelevant, and tell me why you imagine that I can't build a torque gauge that removes all the movement of the meter needle?
(Or even reverses it if I wish to)

[hamdani yusuf (OP)]

DeepSeek R1 answers for the root cause of the problem.

Thinking...
>
>
> Alright, let's tackle the root cause question. The user already knows that rotational units have some issues and possible solutions, so now they want the underlying reason.
>
> First, I need to connect back to the previous problems mentioned: radians being dimensionless, torque vs. energy unit confusion, etc. The root cause should explain why these issues exist in the first place.
>
> The dimensionless nature of radians is a key point. Angles in radians are defined as the ratio of arc length to radius, which are both lengths. So radians are (meter/meter), making them unitless. This is mathematically consistent but leads to situations where angular quantities don't carry a unit, which can be confusing when converting between linear and rotational motion. For example, ω (rad/s) multiplied by r (m) gives m/s, but the radian's absence might make it unclear how the units work out.
>
> Another angle is that the SI system is built around base units, and angles aren't considered a base quantity. Since angle is dimensionless, derived units like radians are treated as derived units without their own dimension. This leads to torque (N?m) and energy (J) sharing the same unit because both involve force and distance, but they're different physically. The system's structure doesn't account for the directional aspects (vector vs. scalar), so the units don't differentiate them.
>
> So the root cause is likely the treatment of angular measure as a dimensionless quantity in the SI system. This design choice simplifies equations but causes ambiguities in unit analysis and physical interpretation. The system prioritizes mathematical consistency over intuitive unit distinction for rotational vs. linear quantities and different physical concepts like torque and energy.
>


The root cause of the problems with rotational quantities lies in **the SI system's treatment of angular measure as a dimensionless quantity**. This stems from: 

1. **Radians as a Ratio**: 
   Radians are defined as the ratio of arc length to radius (both in meters), resulting in a dimensionless unit. While mathematically consistent, this obscures the physical distinction between angular and linear motion in unit analysis. For example, angular velocity (rad/s) appears unitless in equations like \( v = \omega r \), masking the role of rotation. 

2. **Ambiguity in Derived Units**: 
   - Torque (N?m) and energy (J) share the same SI unit, despite representing fundamentally different concepts (rotational force vs. scalar work). 
   - Moment of inertia (kg?m?) uses the same units as other rotational/linear quantities, but its physical meaning (rotational mass) is distinct. 

3. **Dimensional Omission**: 
   The SI system does not recognize angle as a base quantity with its own dimension. This simplifies equations by keeping radians dimensionless but sacrifices clarity in distinguishing rotational phenomena from linear ones. 

In essence, the system prioritizes mathematical simplicity (via dimensionless angles) over intuitive physical differentiation, leading to ambiguities in interpretation and unit analysis.

[hamdani yusuf (OP)]

The only one coming to wrong conclusions is YOU.

What's your answer to the poll?

[hamdani yusuf (OP)]

BC, he will not answer your question. He tries to divert the discourse when questioned after saying something he cannot back up. He has avoided my question, re the "cancellation" of force.

I know. And that's why I can't understand why the mods don't ban him.

Perhaps because they already understand my point. You are wondering why because you haven't yet.

You.
Did.
Not.
Answer.

Read my answer in reply#863. If you can't understand it, that's your problem.

That's the post in which you quoted me saying "(or, if you want, slightly higher)." but ignored it.
So.
Stop wasting time with nonsense about Cavendish's torsion balance- which is very clever but irrelevant, and tell me why you imagine that I can't build a torque gauge that removes all the movement of the meter needle?
(Or even reverses it if I wish to)

You need to understand about the open loop and close loop control systems. I just posted a new video in my other thread.

[alancalverd]

Most of the values contained in the tables are identical with existing widely accepted standard.

and some of them aren't - the ones that produce nonsense when θ = 0

The statement that you quoted is from a user of stackexchange.com,

It's still wrong. Torque is a cause, not an effect.

f you've already used your own common sense, experience, understanding of basic physics and mathematics, and the standard nomenclature that everyone else uses, but still come into a wrong conclusion, then you need to check your underlying assumptions you've used to make that conclusion.

The wheels are still attached to my car. If I had used your definition of torque, they would have fallen off. And the parking brake works on a hill, despite your inability to calculate the pad force.

Torque (N.m) and energy (J) share the same SI unit,

Obviously not - ipsi dixit!. Torque is always stated in newtonmeters, and energy in joules. Dimensionally equivalent, but like length and circumference,  not the same thing,

[Bored chemist]

BC, he will not answer your question. He tries to divert the discourse when questioned after saying something he cannot back up. He has avoided my question, re the "cancellation" of force.

I know. And that's why I can't understand why the mods don't ban him.

Perhaps because they already understand my point. You are wondering why because you haven't yet.

You.
Did.
Not.
Answer.

Read my answer in reply#863. If you can't understand it, that's your problem.

That's the post in which you quoted me saying "(or, if you want, slightly higher)." but ignored it.
So.
Stop wasting time with nonsense about Cavendish's torsion balance- which is very clever but irrelevant, and tell me why you imagine that I can't build a torque gauge that removes all the movement of the meter needle?
(Or even reverses it if I wish to)

You need to understand about the open loop and close loop control systems. I just posted a new video in my other thread.

You need to realise that I understand them better than you do.
Then you need to learn from what I told you about using a computer to get a more or less arbitrary  arbitrary  torque/ position function.

Then you need to think about it, and keep doing so until you see why it's possible to make a torque meter where a clockwise torque produces an anticlockwise rotation.

[paul cotter]

Hamdani reckoned we needed to understand differential calculus. Now he says control systems- we understand and use such systems regularly with loop gain, Nyquist stability criteria, PID, bandwidth, s parameters, Bode plots, etc, etc. Does he think we are all uneducated? 

[Bored chemist]

I'm not sure. I think he believes that, because we don't agree with his interpretation of things like calculus, we don't understand them.

What he doesn't seem able to grasp is that we disagree because he is wrong.

Classic Dunning?Kruger effect

[alancalverd]

Apparently all the control systems I ever designed actually depended on  a resident Good Fairy rather than an intimate knowledge of applied calculus. Not that it is in any way relevant to wheel nuts or brake pads which, according to HY, work by not actually working.

[hamdani yusuf (OP)]

and some of them aren't - the ones that produce nonsense when θ = 0

Then why did you say that all of them are false?

[hamdani yusuf (OP)]

The statement that you quoted is from a user of stackexchange.com,

It's still wrong. Torque is a cause, not an effect.

It's not the error of Gemini.
Torque is caused by a force when the direction doesn't intersect with the axis of rotation.
The force itself is caused by something else.

[alancalverd]

Then why did you say that all of them are false?

because apples are not oranges.

[alancalverd]

The statement that you quoted is from a user of stackexchange.com,

It's still wrong. Torque is a cause, not an effect.

It's not the error of Gemini.
Torque is caused by a force when the direction doesn't intersect with the axis of rotation.
The force itself is caused by something else.

The fact remains that torque is not "a force caused by rotation".

[hamdani yusuf (OP)]

Then why did you say that all of them are false?

because apples are not oranges.

At least some of them must be correct because they are the same as current standard, which you claimed to be perfect.

[hamdani yusuf (OP)]

What exactly is a tensor?

Chapters:
00:00 What exactly are Tensors?
01:23 Analysing conductivity in anisotropic crystals
03:31 Is conductivity a vector? (hint: nope)
05:00 The key idea to understand Tensors
07:07 Rotating the co-ordinate axes (climax)
10:48 Why are Tensors written in matrix form
11:50 Conductivity is a rank-2 Tensor
14:14 Rank-2 Tensors in Engineering & Astronomy
17:48 Rank-3 & Rank 4 Tensors in material science
20:29 The most intuitive definition of Tensors

The rotational inertia is explained at around 15:00.